Subgroups — C₁₃×PSL(2,𝔽₁₃) #28382529

Order 14196.

34 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	PSL(2,𝔽₁₃)	C₁₃	1	1	yes	maximal, characteristic, direct product factor
2	C₁₃×D₁₃⋊C₃	—	14	1	no	maximal
3	C₁₃×C₁₃⋊C₃	—	14	1	no	Hall
4	C₁₃×D₁₃	—	14	1	no	—
5	C₁₃×D₇	—	78	1	no	maximal
6	C₁₃²	—	14	1	no	Sylow
7	C₂×D₃×C₁₃	—	91	1	no	maximal
8	A₄×C₁₃	—	91	1	no	maximal
9	C₇×C₁₃	—	78	1	no	—
10	C₂×C₃×C₁₃	—	91	1	no	—
11	D₃×C₁₃	—	91	2	no	—
12	D₁₃⋊C₃	—	14	1	no	—
13	C₂²×C₁₃	—	91	1	no	—
14	C₃×C₁₃	—	91	1	no	—
15	C₁₃⋊C₃	—	14	1	no	—
16	C₂×C₁₃	—	91	1	no	—
17	D₁₃	—	14	1	no	—
18	D₇	—	78	1	no	—
19	C₁₃	—	14	1	no	—
20	C₁₃	—	84	2	no	—
21	C₁₃	PSL(2,𝔽₁₃)	1	1	yes	maximal normal, characteristic, direct product factor
22	C₂×D₃	—	91	1	no	Hall
23	A₄	—	91	1	no	Hall
24	C₇	—	78	1	no	Sylow
25	C₂×C₃	—	91	1	no	—
26	D₃	—	91	2	no	—
27	C₂²	—	91	1	no	Sylow
28	C₃	—	91	1	no	Sylow
29	C₂	—	91	1	no	—

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. PSL(2,𝔽₁₃)	C₁₃	direct (N × H)
21. C₁₃	PSL(2,𝔽₁₃)	direct (N × H)

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.